Question

Consider the following competing hypotheses and relevant summary statistics: Use Table 4.

H0:	σ21/σ22σ12/σ22 ≥ 1
HA:	σ21/σ22σ12/σ22 < 1

Sample 1: s21s12 = 1,370, and n₁ = 23

Sample 2: s22s22 = 1,441, and n₂ = 15

a.	Calculate the value of the test statistic. Remember to put the larger value for sample variance in the numerator. (Round your answer to 2 decimal places.)

Test statistic

b-1.

Approximate the critical value at the 10% significance level.

	2.05 < critical value < 2.14
	2.17 < critical value < 2.25
	1.64 < critical value < 1.73
	1.81 < critical value < 1.90

    

b-2.

Interpret the results.

	Do not reject H0; we cannot say that variance 1 is lower than variance 2
	Do not reject H0; we can say that variance 1 is lower than variance 2
	Reject H0; we cannot say that variance 1 is lower than variance 2
	Reject H0; we can say that variance 1 is lower than variance 2

Answer 1

s₁² = 1370, n₁ = 23, df₁ = 23-1 = 22

s₂² = 1441, n₂ = 15, df₂ = 15-1 = 14

Since the variance of sample 2 greater than sample 1, the hypothesis can be written as

The Hypothesis:

H0:

Ha:

This is a Right Tailed test

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(a) The Test Statistic:

F = s₂²/s₁² = 1441/1370 = 1.05

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(b-1) The Critical Value: at = 0.01, df1 = 14, df2 = 22, the critical value is 1.825

Therefore OPTION 4: 1.81 < Critical Value < 1.90

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(b - 2) Since t observed is < t critical, Option 4: Reject H0.We can say that variance 1 is lower than variance 2.

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